Geodesic
Twistor transforms of quaternionic functions and orthogonal complex structures
Journal of the European Mathematical Society, Tome 16 (2014) no. 11, pp. 2323-2353.

Voir la notice de l'article provenant de la source EMS Press

The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains Ω of R4. When Ω is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which Ω is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space CP3.
DOI : 10.4171/jems/488
Classification : 53-XX, 00-XX, 14-XX, 30-XX
Keywords: Orthogonal complex structures, quaternions, regular quaternionic functions, twistor methods 
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     title = {Twistor transforms of quaternionic functions and orthogonal complex structures},
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Graziano Gentili; Simon Salamon; Caterina Stoppato. Twistor transforms of quaternionic functions and orthogonal complex structures. Journal of the European Mathematical Society, Tome 16 (2014) no. 11, pp. 2323-2353. doi : 10.4171/jems/488. http://geodesic.mathdoc.fr/articles/10.4171/jems/488/

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